Harry Redknapp said that Tottenham Hotspur were "dreaming an impossible dream" after he watched his team reach the Champions League quarter-finals at the expense of Milan.

There was no little irony in the fact that Tottenham wriggled through after a nervy 0‑0 draw against the seven-times winners, given the manner in which their attacking football has lit up Europe on their debut campaign in the competition. However, despite failing to enjoy the 90 minutes because of the tension, Redknapp could savour the result, which was secured by Peter Crouch's away goal in the first leg at San Siro, and the progress he has overseen. He rarely tires of reminding people that Tottenham were bottom of the Premier League with two points from eight games when he took over, in October 2008.

"I don't know how far we can go but we've done very well to make the last eight," the manager said. "If you'd have said that two years ago, people would have said you were crazy. It's a fantastic achievement and we deserve to be here. We won our group featuring the defending champions Inter and we've kept two clean sheets against AC Milan.

"I think the fans are already dreaming. What we've achieved is an impossible dream. Nobody could have seen this coming. To win as tough a group as there was and then to beat Milan, who are top of Serie A … anything else is a bonus. The fans have got to enjoy it and see what comes."

The quarter-final draw, on Friday week, could pit Tottenham against Barcelona, the conquerors of Arsenal, and there was talk inside the dressing room that they would relish taking on all-comers, even the Spanish champions. Another feature of the evening was the crowing in the stands that Tottenham had gone further in the competition than Arsenal.

Redknapp, though, was more measured in what he wished for. "Barcelona gave one of the finest performances I've ever seen [against Arsenal]. They are amazing. Arsenal are a great team who pass teams to death in our league but they looked out of their depth. Barça were on another level. They are the team you don't want to play at the moment.

"For Barcelona to play against a side that keeps the ball and are the best passing team in the Premier League and make them look so ordinary was amazing. Anybody beating Barcelona would be really difficult. But who knows?"

Massimiliano Allegri, the Milan coach, said that his team's exit had left a "bitter taste". He said: "Over the two games I felt we deserved a bit more."

Redknapp rarely allows himself to get carried away. "I'll just have a bacon sandwich, a cup of tea and take my dogs out. I've had ups and downs, life is a roller-coaster and I try not to get too down or go overboard. It's about the fans. It was a great night for them. The players are in tomorrow for a warm-down. There's no time to celebrate."

He said he "enjoyed the occasion but not the 90 minutes" and said: "It was always going to be nervy. If people thought we were going to smash Milan out of sight, they've not been watching football. We were playing AC Milan, who are top of Serie A and have lost only three games all season, not Raggy-Arsed Rovers."

The goalkeeper, Heurelho Gomes, and the central defenders, William Gallas and Michael Dawson, excelled for Spurs. But the defensive midfielder Sandro was arguably the star. "Sandro was immense," Redknapp said. "He's a young player with a big future."